Replicate Animation with AN 2.1
We start by creating a helix using the following equation:

$$
\begin{aligned}
x &amp;= \cos{ft}\\
y &amp;= \sin{ft}\\
z &amp;= t
\end{aligned}
$$

Where $t\in[-1, 1]$ and $f$ is a factor of frequency. This is implemented in Animation Nodes as follows:



We then vary the radius of the helix such that it lies on a unit sphere. To do so, we note that since $t\in[-1,1]$ represents the z location of the points, then $\sqrt{1-t^2}$ represents the $x$ location of the point if the point lie on a unit circle, or in our case, a cross-section of a unit sphere. This is due to the fact that:

$$
\cos^2{t} + \sin^2{t} = 1
$$

Hence our equation become:

$$
\begin{aligned}
x &amp;= \sqrt{1-t^2}\cos{ft}\\
y &amp;= \sqrt{1-t^2}\sin{ft}\\
z &amp;= t
\end{aligned}
$$

which can be implemented as follows:



This gives us only half of the spiral, to get the full spiral, we flip the spiral and combine it with the original as follows:



We then use those vectors to construct a spline:



We then replicate the output spline by rotating it along the z axis with angles of:

$$
\frac{i\pi}{n} \ \forall \ i \in \{0\dots n-1\}
$$

Where $n$ is the number of splines. This is implemented as follows:



Which gives this result: